Mechanical wave filter



Oct. 19, 1943. R. A. sYKEs MECHANICAL WAVE FILTER Filed Sept. 11, 1942FREQUENCY FIG. 4

t; msousucr ATTORNEY Patented Oct. 19, 1943 UNITED STATES iATENT OFFICETelephone Laborator York, N. Y., a corpora ics, tion of New YorkIncorporated, New

Application September 11, 1942, Serial No. 457,964

19 Claims.

This invention relates to mechanical wave filters and more particularlyto those which comprise a transverse member adapted for flexuralvibration.

The principal object of the invention is to crease the attenuationobtainable with a mechanical wave filter which employs a singletransverse member.

The mechanical wave filter in accordance with the invention comprises acentral rod of acoustic material and a centrally located transversemember adapted to he set into flexural vibration when longitudinalvibration are impressed upon an end of the rod. The transverse membermay. for example, be a crossbar or a disc driven at its center. A peakof attenuation will occur at each frequency at which the transversemember has a fiexural antiresonance. Heretofore, in filters of thistype, only the first antiresonance has been utilized, thus providingonly one attenuation peak. In accordance with the present invention,however, a single transverse member is made to provide two peaks ofattenuation, thus sub stantially doubling the attenuation at allfrequencies away from the peaks. this, the transverse member is sodesigned that it has a fiexural resonance, usually the first, at afrequency for which the central rod is approximately a half wave-length.The two peaks occur at the fiexural antiresonances on each side of thisfrequency. The transmission band extends on both sides of this frequencyand, for a given rod, has a width which decreases as the mass of thetransverse member is increased. A simple graphical method of determiningthe cut off frequencies is presented.

The nature of the invention will be more fully understood from thefollowing detailed description and by reference to the accompanyingdrawing in which like reference characters refer to similar orcorresponding parts, and in which:

Fig. 1 is a perspective view of one embodiment of the invention in whichthe transverse member is a crossbar;

Fig. 2 is a perspective view of another embodiment employing a disc asthe transverse member;

Fig. 3 gives curves from which the cut-off and peak frequencies may befound; and

Fig. 4 is a typical attenuation-frequency characteristic of the filter.

Taking up the figures in more detail, Fig. 1 shows in perspective amechanical filter comprising a central rod l and a centrally locatedtransverse member 2, both made of acoustic ma- To accomplish terial. Thetransverse member 2 is adapted to be set into vibration in the flexuralmode by longitudinal vibrations impressed upon one end of the rod I. Asshown in Fig. 1, the member 2 is in the form of a crossbar which extendsequal distances on each side of the rod 1. Other forms of the transversemember 2 may, however, be employed, so long as they are adapted forfleXural vibration. The rod l and the crossbar 2, as

\ shown, have rectangular cross sections, but other forms of crosssection, such, for example, as circular, may be used equally well.

The cross-sectional dimensions of the rod l are small compared to itslength A, which is approximately a half wave-length at some chosenfrequency is falling within the band to be transmitted. As shown, therod l and the crossbar 2 have the same thickness '5, but it is to beunderstood that they may differ in this dimension. The transverse member2 is designed to have a fiexural resonance coinciding with the frequencyis. When this member is a crossbar of rectangular cross section drivenat its center, as shown in Fig. 1, and the first fiexural resonance isemployed, as is usually the case, the width C and the length D may beproportioned in accordance with the approximate formula:

4.72 1rCV 10.08CV (1) ZVTZD D2 where V is the velocity of propagation inthe acoustic material and is equal to the square root of the ratio ofYoungs modulus Y to the density M.

The peaks of attenuation will occur at the frequencies of fiexuralantiresonance in the transverse member 2. In the embodiment shown inFig. 1 the first antiresonance will be at the frequency f1, below is,given approximately by the formula:

widen 2 The second antiresonance will be on the upper side of is, at thefrequency is, which may be found from the approximate formula:

It is seen from Equations 1, 2, and 8 that, for the crossbar type offilter shown in Fig. 1, the first peak occurs at about 0.63f3 and thesecond peak at about Ms.

Fig. 2 shows in perspective another embodiment of the invention in whichthe central rod I has a circular cross section of diameter E and thetransverse member is a disc 3 having a di ameter and a thickness G. Thedisc 3 is located at the center of the rod i, with its facesperpendicular to the longitudinal axis thereof. When driven in fiexureat its center the disc 3 will have an impedance characteristic whichexhibits resonances and antiresonances. The disc 3 is so designed thatits first fiexural reso nance occurs at the frequency f3 within theband. The antiresonant frequencies determine the peaks of attenuation.The frequencies fm of resonance and antiresonance for the disc 3, corresponding to the different fiexural modes of vibration, are givenapproximately by the formula:

where P is Poissons ratio and the value of k, which involves thediameter F, is found for each of the modes of interest by the solutionof an equation involving Bessel functions, as explained, for example, inthe Philosophical Magasine and Journal of Science, series '7, vol. 24,No. 165, December 1937, pages 1041 to 1055.

The transmission band of the filter cuts oil at the frequencies where w;W' TZI, in which Z0 is the characteristic impedance of the rod 1; Z1 isthe impedance of the transverse member when driven in fiexure at itscenter; o is equal to 21r times the frequency f; and :i is thequadrantaloperator. In Fig. 5, the broken line curve 5 shows thecharacteristic of and I tan W and the solid line curve 6, thecharacteristic of both plotted against the frequency for a typicalfilter. Since the curves 5 and 8 have ordihates which are equal inmagnitude but opposite in sign at the frequencies 1: and f4, these are,therefore, respectively, the lower and upper cutoffs. For a given rod I,the width of the band decreases with an increase in the mass of thetransverse member. For narrow bands, therefore, the disc 3 is to bepreferred to the crossbar 2. The peaks of attenuation occur at thefrequencies f1 and is at which the impedance Z1, and therefore curve 6,is infinite. A typical attenuation characteristic is shown in Fig. 3,with cut-off and peak frequencies marked.

The image impedance Z of the filter, given by the formula is generallymade to match the impedance of the terminal load at the frequency iswithin the band.

What is claimed is:

1. A mechanical wave filter for transmitting a band of frequenciescomprising a central rod and a transverse member both made of acousticmaterial, said rod having a length equal to a half wave-length at afrequency within said band and said transverse member being located nearthe center of said rod and having a fiexural reschance approximately atsaid frequency.

2. A filter in accordance with claim 1 in which said fiexural resonanceis the first.

3. A filter in accordance with claim 1 in which said transverse memberis a crossbar extending equal distances on each side of said rod.

4. A filter in accordance with claim 1 in which said transverse memberis a disc mounted at its center.

5. A filter in accordance with claim 1 in which the cross-sectionaldimensions of said rod are small compared to its length.

6. A filter in accordance with claim 1 in which said flexural resonanceis the first and the crosssectional dimensions of said rod are smallcompared to its length.

7. A mechanical wave filter for transmitting a band of frequenciescomprising a central rod and a crossbar both made of acoustic material,said rod haVing a length equal to a half wavelength at a frequencywithin said band and said crossbar being located near the center of saidrod and having a flexural resonance approximately at said frequency.

8. A filter in accordance with claim 7 in which said flexural resonanceis the first.

9. A filter in accordance with claim 1 in which said rod and saidcrossbar have the same thickness.

10. A filter in accordance with claim 7 in which said rod and saidcrossbar have rectangular cross sections of the same thickness.

11. A filter in accordance with claim 7 in which said fiexural resonanceis the first and said rod and said crossbar have the same thickness.

12. A filter in accordance with claim '7 in which said fiexuralresonance is the first and said rod and said crossbar have rectangularcross sections of the same thickness.

13. A filter in accordance with claim '7 in which said flexuralresonance is the first and the cross-sectional dimensions of said rodare small compared to its length.

14. A filter in accordance with claim '7 in which said flexuralresonance is the first, the cross-sectional dimensions of said rod aresmall compared to its length and said rod and said crossbar have thesame thickness.

15. A filter in accordance with claim 7 in which said fiexural resonanceis the first, the cross-sectional dimensions of said rod are smallcompared to its length and said rod and said crossbar have rectangularcross sections of the same thickness.

16. A mechanical wave filter for transmitting a band of frequenciescomprising a central rod and a transverse disc both made of acousticmaterial, said disc being mounted at its center perpendicularly to thelongitudinal axis of said rod and having a fiexural resonance at afrequency within said band.

17. A filter in accordance with claim 16 in which said fiexuralresonance is the first.

18. A filter in accordance with claim 16 in which said rod has a lengthapproximately equal to a half wave-length at said frequency and saiddisc is located near the center of said rod.

19. A filter in accordance with claim 16 in which said flexuralresonance is the first, said rod has a length approximately equal to ahalf wavelength at said frequency and said disc is located near thecenter of said rod.

ROGER A. SYKES.

